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A simple proof that super-reflexive spaces are $K$-spaces

Author(s): Félix Cabello Sánchez
Journal: Proc. Amer. Math. Soc. 132 (2004), 697-698.
MSC (2000): Primary 46B03, 46B08, 39B82
Posted: September 29, 2003
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Abstract: We demonstrate the title.

References:

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N. Kalton, Nonlinear commutators in interpolation theory, Memoirs of the American Mathematical Society, vol. 73, no. 385, 1988. MR 89h:47104

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N. Kalton, N. T. Peck, and J. W. Roberts, An F-space sampler, London Mathematical Society Lecture Note Series 89, Cambridge University Press, Cambridge, 1984. MR 87c:46002

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N. Kalton and J. W. Roberts, Uniformly exhaustive submeasures and nearly additive set functions, Trans. Amer. Math. Soc. 278 (1983) 803-816. MR 85f:28006

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M. Ribe, Examples for the nonlocally convex three space problem. Proc. Amer. Math. Soc. 73 (1979) 351-355. MR 81a:46010

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J. W. Roberts, A nonlocally convex $F$-space with the Hahn-Banach approximation property, in: Banach spaces of analytic functions, Springer Lecture Notes in Mathematics 604, Berlin-Heidelberg-New York (1977) 76-81. MR 58:30008

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B. Sims, ``Ultra''-techniques in Banach space theory. Queen's Papers in Pure and Applied Mathematics 60, Queen's University, Kingston, Ontario, Canada, 1982. MR 86h:46032

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Additional Information:

Félix Cabello Sánchez
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, Spain
Email: fcabello@unex.es

DOI: 10.1090/S0002-9939-03-07180-6
PII: S 0002-9939(03)07180-6
Keywords: $K$-space, super-reflexivity, ultraproduct
Received by editor(s): June 20, 2001
Posted: September 29, 2003
Additional Notes: Supported in part by DGICYT project BMF 2001---083.
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2003, American Mathematical Society

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